NEWTON’S LAWS via ART –
PART II
Abraham Tamir
Newton’s Second Law: law of acceleration
Newton's First Law deals with an object with no
net force. Newton's
Second Law talks about an object that has net force acting on it.
Firstly, the law states that if you do place a force on an object, it will
accelerate, i.e., change its velocity, and it will change its velocity in the
direction of the force. Secondly, this acceleration is directly
proportional to the force. For example, if you are pushing on an object,
causing it to accelerate, and then you push, say, three times harder, the
acceleration will be three times greater. Thirdly, this acceleration is
inversely proportional to the mass of the object. For example, if you are pushing
equally on two objects, and one of the objects has five times more mass than
the other, it will accelerate at one fifth the acceleration of the other.
The Second Law formulated at about 1792 gives us an exact relationship between
the net force F acting on a body, its mass m, and the
acceleration a of the body due to the force. It can be expressed as a
mathematical equation by FORCE = MASS times ACCELERATION, namely
F = ma
The
equation is very aesthetic since all the powers in it are exactly 1. The
following are the definitions of the quantities in the above formula that are
demonstrated below by different artworks.
The force F is anything that can cause a massive body to accelerate. It may
be experienced as a lift, a push, or a pull. Force was first mentioned by
Archimedes in the 3rd century BC but only mathematically defined by Isaac Newton in the 17th century.
Force was first mentioned by Archimedes
in the 3rd century
BC but only mathematically
defined by Isaac Newton
in the 17th century.
Fig.15: Demonstrations
of the Force F
Figs.
15 and 16 are artistic demonstrations of force F where Rene Magritte painted
the picture on the left-hand-side of Fig.15; the other pictures are by unknown
artists.
Fig.16: Demonstrations of
Force F
Mass is a fundamental
concept, roughly corresponding to the intuitive idea of "how much matter
there is in an object". Mass m is usually defined as the
quantity of matter in a body, its inertia, or resistance to acceleration.
Fig.17 are different artistic demonstrations of
mass. On top-left is a sculpture photographed by the author in Coruna – Spain where top-right was photographed in a
gallery in Paris.
Bottom-left was painted by the Austrian De
Fig.17: Demonstrations of Mass m
Es Schwertberger (b.1942), a myth
and mystery artist. On
bottom-right is an artwork by Fernando Botero. Fig. 18 demonstrates
masses approaches infinity (Left) and masses approaching zero (Right). On
the left-top is a sculpture by Fernando Botero where on right-top is a
sculpture by Alberto Giacometti (1901-1966), a Swiss surrealist painter and
sculptor. The author photographed the picture in the bottom.
Fig.17: Mass approaching
infinity (Left) and Mass approaching zero (Right)
Finally the concept of acceleration
a is
demonstrated via art by falling bodies. a is defined by the rate at which an object's velocity
changes with time. On the left-hand-side is an artwork of falling drops
by Anatoli Fomenko (b.1945), a Ukraine
scientist-art & mathematics.
Fig.18. Demonstration of
acceleration
Fig.19 demonstrates Newton’s Second Law by a
single artwork. The artwork on the left was painted by Franz Stuck (1863 -1928), a German Symbolist/Art Nouveau painter, sculptor, engraver, and architect. The
artwork in the middle is a sculpture constructed by Rafi Carasso (b.1945), an
Israeli medical doctor and artist. Fernando Botero painted the image on
the right.
Fig.19. Newton’s Second Law F = mg
Newton’s Third Law: Action = Reaction
Newton's Third Law of motion states: ”all
forces in the universe occur in equal but oppositely directed pairs”.
There are no isolated forces; for every external force that acts on an object
there is a force of equal magnitude but opposite direction that acts back on
the object, which exerted that external force. In
other words “when one body exerts a force on the other, then the second body
exerts a force equal in magnitude and opposite in direction on the first body,
namely, action = reaction.” Thus, in the interaction between a system and
its surroundings, forces always appear in pairs where each force acts on the
other body. This is also the reason why they do not cancel each other.
We usually do not pay attention to
the fact that this law is active at “every corner”, and that every time we
interact with our surroundings we feel the law. The following are a few
examples. When you punch someone in the face, your hand not only applies
a force to the person's face; the person's face applies a force to your
hand. Since the person's face is softer than your hand it suffers
more from the interaction. When we press our lips one against the other
we feel some pain in both lips because of the force that is exerted. When
we stand on the floor we feel our weight (the action) only due to reaction of
the floor on our legs. Sprinters usually apply some force with their legs
on some slanted objects. The reaction force of the object, according to Newton’s Second Law,
provides an initial acceleration to the sprinter, which is proportional to his
mass. As far as it looks surprising, a falling body attracts earth
upwards at the same force as earth attracts the body downwards.
However, since earth acceleration upwards is much smaller than acceleration g
it is impossible to see any motion of earth. The Third Law is very
important for space travel. In the cold void of space there is no air for
jets to suck or for propellers to churn, and yet space ships can maneuver in a
vacuum. How do they do it? The engines propel gas particles out the back
of the space ship. Since every force has an equal and
opposite reaction force, the space ship will be propelled forwards.
Because of the First Law, space ships do not need very much fuel - once they
are moving they will stay in motion because friction, the opposing force, is
negligible. A bird flies by use of its wings.
The wings of a bird push air downwards. In turn, the air reacts by pushing the
bird upwards. The size of the force on the air equals the size of the
force on the bird; the direction of the force on the air (downwards) is
opposite to the direction of the force on the bird (upwards). An automobile is
equipped with wheels that rotate backwards. As the wheels rotate backwards,
they push the road backwards. In turn, the road reacts by pushing the
wheels forward. The size of the force on the road equals the size of the force
on the wheels; the direction of the force on the road (backwards) is opposite
to the direction of the force on the wheels (forwards). Thus
action-reaction force pairs make it possible for automobiles to move as well as
birds
to fly.
In the
following, Newton’s Third Law is demonstrated by different artworks
that describe different applications of the law. Fig.20 is a sculpture
constructed by Dudu Geva (1950-2005), Israeli caricaturist. The sculpture
is of David Ben-Gurion (1886-1973), Zionist leader,
founder of the state of Israel
and Israel's
first and longest-serving Prime Minister. The original sculpture is on
the left-hand-side, however both cases demonstrate
different possibilities of the third law. Fig.20 is an artwork of
Fernando Botero. In addition to the marked places where the law is
active, it takes place also between the leaning head of the woman and her palm
or between the fingers of the woman and the plate she is holding.
Figs.22, 23 are additional demonstrations of the Law. Fig.23 left is a caricature
of the Israeli Minister Fuad Ben Eliezer painted by the Israeli caricaturist
Moshik Lynn (b.1950). Note that
when Fuad is closing his mouth, identical forces in opposite directions are
created between the two lips. Fig.24 demonstrates the idea that Newton’s Laws are
applicable not only on earth but also on other galaxies. On the picture
of Callisto, the moon of the planet Jupiter, the
author “transplanted” on each of the above stars the dancing couple of Botero
that demonstrates Newton’s
Third Law. The only difference between the two stars is that on Jupiter,
the action created by the weights of the bodies will be higher by a factor of
two because the acceleration gravity on it, 2.45 m/s2, is higher by
a factor of two than on Callisto.
Fig.20. Newton’s Third Law: Action = Reaction
Fig.21. Newton’s Third Law
Fig.22. Newton’s Third Law
Fig.23. Newton’s Third Law
Fig.24. Newton’s Third Law is
applicable everywhere in the universe
Fig.25. What happens without
reaction?
Fig.25 demonstrates what may happen if reaction
would not have existed when reaction
takes place. So what happens is that the cup of
coffee will penetrate into the brain as seen by the X-ray view created by the
author. Terrible!!! So we may thank God that created order in our
universe, for example action = reaction as well as the other laws.
As in Newton’s First Law, the following cases
demonstrate qualitatively Newton’s
Third Law. For example Fig.26 of the British fantasy art
painter Brian Froud (b.1947) demonstrates the following saying in psychology:
“Don’t push too hard (action) because there will be a reaction”.
Fig.26: Newton’s
Third Law demonstrated qualitatively
Fig.27 is another
example demonstrating action = reaction that was painted by the American Alex
Grey (b.1953), an anatomy of the body artist.
Fig.27: Newton’s
Third Law:
Action: He loves her. Reaction: She loves him
Fig.28 is the final example
demonstrating qualitatively Newton’s
Third Law according to which: Action: Invest in education. Reaction: You
will raise Einsteins.
Fig.28: Newton’s
Third Law
Newton’s Universal Law of Gravity
The major assumption in Newton’s universe was
that the mass m of a body is the major factor in the formation of the “Gravity
Force” F where in the absence of mass there is no gravity.
Fig.29. The Solar System
According to “Newton’s
General Law of Gravitation” the force F between two masses is
defined by
F = m1m2/r2
where m1 and m2 are the masses of
the two bodies and r is the distance between them. The equilibrium between the
above force and m(v2/r) - the centrifugal
force, keeps all bodies in a stable circular motion. Fig.29, painted by
the American Ron Miller (b.1947), an artist and author of astronomical books,
demonstrates the Solar System and gives the impression of the above stable
equilibrium.
In conclusion it is
expected that the above demonstrations by art of Newton’s laws make them more understandable,
perceptible and easy to remember.
